Solution 5 B1 is the key play!
Although the White corner stones were already within Black’s Sector Line, with W1 (or “a”, “b”, or “c”) White could easily have cut that Sector Line and thus put the baseless (= weak) Black 7- stone group on the left in danger.
Instead, the simple B1 completely encloses the White corner stones within essentially unbreakable Black Sector Lines, so with still incomplete eyeshape White must do something about that immediately or die!
The key White shape point in the corner is “d”, and a weak player would be well advised to play there immediately to assure White’s eyes.